A BRE E 
RT 
A" 
vez 
  
-1 
T : 
077 z (A,PgA,) cp Min .. (5) 
As it is proved in Rao /18/, the minimum of 077 is obtained when 
T TS il 
Ag; Papa: = +0 ’ J Ao. 171,215.02 (6) 
J z = number of add. parameters 
i.e. for a diagonal weight matrix Ps the optimal choïce of A, TS obtainedj if' the 
columns of A, are orthogonal, not necessarily orthonormal. (Hence orthogonality is 
defined as : AT PA - D, De diagonal matrix). 
Although the concept of orthogonality is strongly valid only in the case of ex- 
tremely regular network arrangements, orthogonal sets provide in practice for the 
best possible independence. 
It is clear that in aerial triangulation systems orthogonality is more likely than 
in close-range systems. 
Fora 3x 3 image point distribution the corresponding orthogonal additional pa- 
rameter set was derived by Ebner /6/. Recently the author developed an orthogonal 
set with respect to a 5 x 5 image point distribution. 
with k= x? = = a opta epa ee PU n° 
"xt rabat. Dat | s» yy EEE V9 M 
we obtain 
AX = à15X + à51y *à55Xy + 8541 *9 0 -b, 194 
7 
P = 10 
Ay = a1oy  * 851X a3 74 0 + bızk *tb55Xy + 
(Ax y + aq Xp 854yk + 845Xl*8,4yq * 0 + 310 + 0 + 0 + 
(Ay.0}:+ma0 + 0 + ,0 + 0 + b14Xp * b,4yktb.,xl * b,,yq+ 
(AX 33) 2 dig *tà54Xyp +a 54k tà,5Xyq* àp1S + 0 +: »0 +3 00 +220 +y 0 + 
(5y..) t D + 0 + D + © + D 
+ 
ber *bo4Xyp*bs44kl*b,,xyqsb, s 
{ax 50) ta,pyr +az4X1p tanz ykqta-„ XS de 30 + i {0 * n) + val ce 
(ay. }» +0 + 0 +" 0 +. Q + D5p yr +D34x1p+b,3ykq+b,2xs+ 
(AX o: tag,ir +à,4XYPG+a,2kS * 0 * :0 +00 + 
(AY) 3 ©0 + 0 + 0 *b4glr +b,4XYP9+b52kS + 
(ax) ta,gYqr+a,,xps + 0 + 0 * agers + OO ; 
(Ay...) + © + 0 +D,gYar+b,4xps+ 0 +b- rs ; 
ej